摘要：This paper presents a new form of quartic equation based on Lagrange’s extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid.A very explicit and concise formulae of the quartic equation by Ferrari’s line is found, which avoids the need of a good starting guess for iterative methods.A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates.The convergence region of the algorithm is investigated and the corresponding correct solution is given.Lastly, the algorithm is validated with numerical experiments. Key words Geodetic coordinates Cartesian coordinates Groebner basis Ferrari’s solution convergence region.
关键词：Geodetic coordinates ;Cartesian coordinates ;Groebner basis ;Ferrari’s solution ;convergence region
